A method of bending glass panes heated to their softening temperature in the horizontal position. The panes are heated to their bending temperature in a furnace. The panes are brought between a concave bending frame having shaping surfaces that describe a smaller contour than dimensions of the panes, and a convex upper form with a solid surface. The panes are pressed between the bending frame and the upper form so that the panes assume, at least at certain points, the contour of the upper form. A ring-shaped final-bending frame having shaping surfaces that correspond to the final shape of the panes is brought into contact with the protruding marginal regions of the panes, and the panes are pressed against the upper form. The panes on which the bending operation has been completed are subjected to a cooling or quenching treatment.